The stress-energy tensor \(S_{F, \omega }\)  associated with the \(\mathcal {E}_{F,g}\) -energy functional is
defined as follows (see [1]}, [2]}, [3]}, [4]}, [5]}):
\(S_{F,\omega }(X,Y)=F(\frac{|\omega |^2}{2})g(X,Y)-F^{\prime }(\frac{|\omega |^2}{2})\langle i_X\omega ,i_Y\omega \rangle \, , \) 
